Turbulence laws in natural bed flows

Abstract

Characterization of turbulence in natural bed streams is one of the most fascinating problems of fluid dynamics. In this study, a statistical description of turbulence in a natural pebble bed flow is presented applying the laws of turbulence. A laboratory experiment was conducted to measure the three-dimensional instantaneous velocity components in a flow over heterogeneous coarse sediments that simulated a natural bed. The analysis reveals that the spectra (in Fourier space) show a power-law scaling, $E(k)\sim k^{{\it\alpha}}$, suggesting the presence of inertial range turbulence. The exponent ${\it\alpha}$ is slightly shallower than the Kolmogorov $5/3$ scaling law, with this deviation possibly due to the bed roughness heterogeneity and to fluctuation anisotropy. The Taylor frozen-in approximation is broken at smaller scales towards the roughness crest level; therefore, a new statistical tool for the validation of this approximation is proposed. The Kolmogorov $4/5$-law for the longitudinal increments and simultaneously the Monin–Yaglom $4/3$-law for the nonlinear normal fluxes (both in physical space) are preserved, providing an accurate estimation of the turbulent kinetic energy dissipation rate. The heterogeneity of the bed acts to induce the transport of finite kinetic helicity to the outer layer through persistently prolonged vortices. An associated $2/15$-law for the cascade of helicity has been locally found. These findings open a new direction in turbulence research for flows over highly rough beds.